Remark 4 The correction term \(E\)  in the proposed flux and position observer (REF ) can be roughly viewed as the gradient descent of the cost function generated from the KRE, rather than the “natural” cost function (REF ) adopted in [1]}. This idea was originally proposed in the pioneer work [2]} to improve transient performance in adaptive observers, for which the unknown parameters are constant. In the context of observer design, we need to take into account the dynamics of the time-varying states, and this is captured by the additional variable \(\xi \)  in the proof.

